Nielsen SoundScan data shows that "Stronger" sold 40 percent fewer copies than the previous week, according to a report from Billboard.com. The album did climb the Billboard 200 albums chart from No. 39 to No. 17, but the report attributes the jump to the overall album market being down 49 percent in sales. "Stronger" saw a smaller decline in sales than other albums on the chart.

In addition, Billboard says the smaller decline is due to digital album sales, which mostly came via iTunes. The report notes Clarkson's album was prominently featured in the iTunes store, where it was on sale for $7.99.

The initial report of Clarkson's rise in sales for "Stronger" came from the album's appearance on Amazon's "Movers & Shakers in Music" chart, which cited the album's sales rising over 400 percent in a matter of 24 hours.

Many of the recent comments about the album on its Amazon page refer to her endorsement of Ron Paul.

"You have balls of steel Kelly! Ron Paul 2012! Thank you for your support and remember that there are plenty of fellow patriots that have your back," a user named Sam wrote on December 30.

However, according to Billboard, the album only sold 600 copies through online stores like Amazon and the sales figures were actually down 72 percent from the previous week.

"I love Ron Paul. I liked him a lot during the last republican nomination and no one gave him a chance," Clarkson wrote on her Twitter page on December 28. "If he wins the nomination for the Republican party in 2012 he's got my vote. Too bad he probably won't."

"I like Ron Paul because he believes in less government and letting the people (all of us) make the decisions and mold our country," she added. "That is all. Out of all of the Republican nominees, he's my favorite."

Clarkson is one of the most successful "American Idol" contestants and is known for fast pop-rock songs that empower women and would likely appeal to those scorned by lovers, including "Miss Independent," Since U Been Gone" and "Behind Those Hazel Eyes."